Good question…
What makes 98.60 degrees normal?
What makes people normal?
Generally, references to a statistical distribution or just a “distribution” mean a “frequency distribution.” That is, what is the number of times or the frequency with which each value in the distribution occurs.
As it turns out, a large percent of all frequency distributions meet the same set of criteria. Such distributions are called “normal.” A more popular term is “bell curve.”
NOTE: “Bell” is not a technical term. However, because the term stuck, for convenience it is used in this series.
These normal types of distributions have many uses in market research and other statistical applications. A lot of statistical theory that applies to market research assumes normal distributions.
Examples of normal distributions in humans include: height; weight; test scores especially for standardized tests such as I.Q.; and various abilities, traits, tastes, and preferences. All assume a large number of people being “measured.” One notable exception is income earned, which will be discussed in the next article with distributions that are not normal.
Normal distributions also are common in both nature and business. For example, light bulb packages have information on the number of hours the bulb should last, the watts (energy used), and the lumens (light output).
Each of those numbers is an arithmetic mean of the frequency distribution generated by testing large numbers of light bulbs. Each of those distributions is bell-shaped or normal.
So what are the criteria for a distribution to be normal?
1) The distribution is unimodal (only one most frequently occurring value).
2) The arithmetic mean, the mode, and the median are all the same value. That value is the value representing the highest point on the distribution;
3) The distribution is bi-laterally symmetrical.
BY WHAT?!
Bi-laterally symmetrical means the left half is a mirror image of the right half (unless you’re left-handed, then the right half is a mirror image of the left half).
4) One standard deviation–hereafter noted as 1�OE –measured each way from the arithmetic mean (what’s referred to as plus or minus one standard deviation or � 1�OE) represents slightly over 68 percent of all the values in the distribution. � 1.96 �OEs represents the middle 95 percent of the values. You can go to readily available tables to see how many standard deviations from the mean are associated with what percent of all the values in the distribution. This percent is often referred to as the “area under the curve.” For instance, � 1�OE covers slightly over 68 percent of the area under the curve. The curve is the graphic representation of the frequency distribution.
and
5) There are some other criteria, but the above ones are the main ones (at least for now).
Normal distributions come in various sizes and shapes but all meet the criteria noted above. Some normal distributions look like they are relatively short and spread out; other normal distributions look relatively tall and thin. The largest percent of all normal distributions are in between those more extreme shapes and are the true bell curves.
In market research, you might want to ask consumers how they would rate the service they received. A properly designed survey would gives choices such as “excellent” “good” “fair” “poor” “very poor.” A future article will deal with the problems of such surveys. The point here is that the choices have to be symmetrical in terms of balancing the choices around the middle of the distribution. The results should produce a normal distribution. If the results are not “normally distributed” you should be suspicious of the results. Contrary to what many are led to think, not everything is good or excellent.
Raoty Paul Official 